6=-5w(w-4)

Solution for 6=-5w(w-4) equation:

Simplifying
6 = -5w(w + -4)

Reorder the terms:
6 = -5w(-4 + w)
6 = (-4 * -5w + w * -5w)
6 = (20w + -5w2)

Solving
6 = 20w + -5w2

Solving for variable 'w'.

Reorder the terms:
6 + -20w + 5w2 = 20w + -20w + -5w2 + 5w2

Combine like terms: 20w + -20w = 0
6 + -20w + 5w2 = 0 + -5w2 + 5w2
6 + -20w + 5w2 = -5w2 + 5w2

Combine like terms: -5w2 + 5w2 = 0
6 + -20w + 5w2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + -4w + w2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -4w + -1.2 + w2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -4w + w2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -4w + w2 = 0 + -1.2
-4w + w2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-4w + w2 = -1.2

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = -1.2 + 4

Reorder the terms:
4 + -4w + w2 = -1.2 + 4

Combine like terms: -1.2 + 4 = 2.8
4 + -4w + w2 = 2.8

Factor a perfect square on the left side:
(w + -2)(w + -2) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(w + -2) equal to 1.673320053 and -1.673320053.

Subproblem 1
w + -2 = 1.673320053

Simplifying
w + -2 = 1.673320053

Reorder the terms:
-2 + w = 1.673320053

Solving
-2 + w = 1.673320053

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + w = 1.673320053 + 2

Combine like terms: -2 + 2 = 0
0 + w = 1.673320053 + 2
w = 1.673320053 + 2

Combine like terms: 1.673320053 + 2 = 3.673320053
w = 3.673320053

Simplifying
w = 3.673320053

Subproblem 2
w + -2 = -1.673320053

Simplifying
w + -2 = -1.673320053

Reorder the terms:
-2 + w = -1.673320053

Solving
-2 + w = -1.673320053

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + w = -1.673320053 + 2

Combine like terms: -2 + 2 = 0
0 + w = -1.673320053 + 2
w = -1.673320053 + 2

Combine like terms: -1.673320053 + 2 = 0.326679947
w = 0.326679947

Simplifying
w = 0.326679947

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.673320053, 0.326679947}